Padm 7060 quantitative methods for public administration unit 3 chapters 9 10
Download
1 / 18

PADM 7060 Quantitative Methods for Public Administration Unit 3 Chapters 9-10 - PowerPoint PPT Presentation


  • 118 Views
  • Uploaded on

PADM 7060 Quantitative Methods for Public Administration Unit 3 Chapters 9-10. Fall 2004 Jerry Merwin. Meier & Brudney Part III: Probability. Chapter 7: Introduction to Probability Chapter 8: The Normal Probability Distribution Chapter 9: The Binomial Probability Distribution

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'PADM 7060 Quantitative Methods for Public Administration Unit 3 Chapters 9-10' - mikkel


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Padm 7060 quantitative methods for public administration unit 3 chapters 9 10

PADM 7060 Quantitative Methods for Public AdministrationUnit 3 Chapters 9-10

Fall 2004

Jerry Merwin


Meier brudney part iii probability
Meier & BrudneyPart III: Probability

  • Chapter 7: Introduction to Probability

  • Chapter 8: The Normal Probability Distribution

  • Chapter 9: The Binomial Probability Distribution

  • Chapter 10: Some Special Probability Distributions


Meier brudney chapter 9 the binomial probability distribution
Meier & Brudney: Chapter 9 The Binomial Probability Distribution

  • What is the binomial probability distribution?

  • What is a Bernoulli process?


Meier brudney chapter 9 the binomial probability distribution page 2
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 2)

  • Let’s discuss the characteristics of a Bernoulli process: (book says two, but can be three)

    • Each trial’s outcome must be mutually exclusive: Success or failure

    • Probability of success (p) remains constant (as does probability of failure, q)

    • Trials are independent (Not affected by outcomes of earlier trials)

    • Examples:

      • Coin flip

      • Roll of die (six or not six)

      • Fire in a community


Meier brudney chapter 9 the binomial probability distribution page 3
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 3)

  • More on Bernoulli process - Must how three things to determine probability:

    • Number of trials

    • Number of successes

    • Probability of success in any trial

  • Formula (see page 146)

    • Combination of n things taken r at a time


Meier brudney chapter 9 the binomial probability distribution page 4
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 4)

  • Let’s look at some examples:

    • Starting at the bottom of page 146:

      • How many sets of three balls can be selected from four balls (a, b, c, d)?

      • How many combinations of four things two at a time?

      • We can list the possibilities with these examples to come up with solutions.


Meier brudney chapter 9 the binomial probability distribution page 5
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 5)

  • What if we do not want to list all the combinations?

    • See the formula on page 147

  • Do you understand how to calculate a factorial?

    • Examples of formula with coin flip (pages 147-149)


Meier brudney chapter 9 the binomial probability distribution page 6
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 6)

  • What is the problem with calculating factorials?

    • Cumbersome in larger numbers!

  • So what alternative do we have?

  • How can the normal curve be used?

    • A general rule‑of‑thumb is that once n ≥ 30, the normal distribution can be used to calculate the binomial probability distribution.


Meier brudney chapter 9 the binomial probability distribution page 7
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 7)

  • How about the problem on the Republican’s chance of being hired in Chicago? (Page 151)

    • See the information for the binomial distribution

    • The standard deviation of a probability distribution at the bottom of 151

    • Simply convert the number actually hired into a z score and look up the value.


Meier brudney chapter 9 the binomial probability distribution page 8
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 8)

  • On page 152, you're told that you should use this only when n x p is greater than 10 and n x (1 -p) is greater than 10.

  • Also, keep in mind that the normal curve tells you the probability only that r or fewer (or more) events occurred. It does not tell you the probability of exactly r events occurring.

  • This probability can be determined only by using the binomial distribution.


Meier brudney chapter 9 the binomial probability distribution page 9
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 9)

  • Problems: 9.2 & 9.6


Meier brudney chapter 10 special probability distributions
Meier & Brudney: Chapter 10 Special Probability Distributions

  • What is the Hypergeometric Probability Distribution and when is it used?

    • When you have a finite population the hypergeometric probability distribution is better than the binomial distribution.


Meier brudney chapter 10 special probability distributions page 2
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 2)

  • Let’s look at the Andersonville City Fire department example (pp. 157-158).

    • There are 34 women out of a pool of 100 eligible applicants.

    • The p = .34, and 30 trials (n = 30).

    • Thus your mean is:  = 30 x .34 = 10.2.

    • The key difference is in computing the standard deviation.

  • The formula is shown on page 158 and the answer is on 159.


Meier brudney chapter 10 special probability distributions page 3
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 3)

  • What is The Poisson distribution?

    • It is named for the Frenchman, Simeon Dennis Poisson, who developed it in the first half of the 19th century.

    • It is used to describe a pattern of behavior when some event occurs at varying, random intervals over a continuum of time, length, or space.

    • Your text uses muggings & potholes as examples.

    • It has been widely used to describe the probability functions of phenomena such as product demand; demand for services; # of calls through a switchboard; passenger cars at toll stations, etc.


Meier brudney chapter 10 special probability distributions page 4
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 4)

  • How is the Poisson distribution different from the Bernoulli process?

    • The number of trials is not known in a Poisson process.

    • Instead, the Poisson distribution is concerned with a discrete, random variable which can take on the values x = 0,1,2,3 . . . where the three dots mean "ad infinitum".

    • The formula is:  = xe-/x! (see page 160)


Meier brudney chapter 10 special probability distributions page 5
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 5)

  • The formula is:  = xe-/x!

    • where:

      •  (lambda) = the probability of an event

      • x = # of occurrences

      • e = 2.71828 (a constant that is the base of the Naperian or natural logarithm system)

  • Fortunately, this is not something we need to calculate;

    • we'll use Table 2 (pp. 444-445), as we are sane.


Meier brudney chapter 10 special probability distributions page 6
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 6)

  • Let’s look at the management example on pages 160-161.

  • Why does the Poisson table only go to 20 for the λvalues?

    • We can use the normal distribution table for those values above 20.


Meier brudney chapter 10 special probability distributions page 7
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 7)

  • Problems 10.2, 10.4, 10.6, & 10.16